共查询到17条相似文献,搜索用时 109 毫秒
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本文将一维Lagrange插值多项式的Newton表达式推广到二维非标准的Hermite插值,给出著名板元-ACM元插值多项式的Newton表达式,由此给出ACM元对四阶和二阶椭圆问题的各向异性插值误差估计,为复杂单元的各向异性分析开辟了新的途径. 相似文献
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本以Newton插值及Thiele型连分式插值为基础,其线性与非线性插值方法相结合,通过混合差商的定义,给出了三元Newton-Thiele型插值公式及误差估计式。 相似文献
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1 引言
一元向量值有理插值问题在[1-5]中有了比较系统的研究.文[6—13]成功地将一无的结果推广到了二元的情形,但它们采用的大多是向量值连分式的方法,且没有给出二元向量值有理插值存在性的判别方法及其证明.本文利用二元Newton插值公式, 相似文献
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牛顿(Newton)插指 总被引:5,自引:0,他引:5
提出了牛顿(Newton)插值问题的一种新形式,幂指数形式,简称牛顿插指.应用这种插指法,可以容易构造出一类离散型总体的一种公式式分布律. 相似文献
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本文以 Newton插值及 Thiele型连分式插值为基础 ,将线性与非线性插值方法相结合 ,通过混合差商的定义 ,给出了三元 Newton-Thiele型插值公式及误差估计式 . 相似文献
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We give a Newton type rational interpolation formula (Theorem 2.2). It contains as a special case the original Newton interpolation, as well as the interpolation formula of Liu, which allows to recover many important classical q-series identities. We show in particular that some bibasic identities are a consequence of our formula. 相似文献
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Summary A method for the construction of a set of data of interpolation in several variables is given. The resulting data, which are either function values or directional derivatives values, give rise to a space of polynomials, in such a way that unisolvence is guaranteed. The interpolating polynomial is calculated using a procedure which generalizes the Newton divided differences formula for a single variable. 相似文献
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The numerical stability of barycentric Lagrange interpolation 总被引:10,自引:0,他引:10
The Lagrange representation of the interpolating polynomialcan be rewritten in two more computationally attractive forms:a modified Lagrange form and a barycentric form. We give anerror analysis of the evaluation of the interpolating polynomialusing these two forms. The modified Lagrange formula is shownto be backward stable. The barycentric formula has a less favourableerror analysis, but is forward stable for any set of interpolatingpoints with a small Lebesgue constant. Therefore the barycentricformula can be significantly less accurate than the modifiedLagrange formula only for a poor choice of interpolating points.This analysis provides further weight to the argument of Berrutand Trefethen that barycentric Lagrange interpolation shouldbe the polynomial interpolation method of choice. 相似文献
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基于等距节点积分公式的牛顿迭代法及其收敛阶 总被引:1,自引:0,他引:1
利用等距节点的数值积分公式构造牛顿迭代法的变形格式.我们证明了利用4等分5个节点的Newton-Cotes公式构造的变形牛顿迭代法收敛阶为3,并进一步证明了对于最常用的3等分4节点、5等分6节点、6等分7节点、7等分8节点积分公式,所得到的变形牛顿迭代法收敛阶都是3.最后,本文猜想,利用任意等分的积分公式构造变形牛顿迭代法,所得的迭代格式收敛阶都是3. 相似文献